Block encoding bosons by signal processing
Block Encoding (BE) is a crucial subroutine in many modern quantum algorithms, including those with near-optimal scaling for simulating quantum many-body systems, which often rely on Quantum Signal Processing (QSP). Currently, the primary methods for constructing BEs are the Linear Combination of Un...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-05-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-05-15-1747/pdf/ |
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| author | Christopher F. Kane Siddharth Hariprakash Neel S. Modi Michael Kreshchuk Christian W Bauer |
| author_facet | Christopher F. Kane Siddharth Hariprakash Neel S. Modi Michael Kreshchuk Christian W Bauer |
| author_sort | Christopher F. Kane |
| collection | DOAJ |
| description | Block Encoding (BE) is a crucial subroutine in many modern quantum algorithms, including those with near-optimal scaling for simulating quantum many-body systems, which often rely on Quantum Signal Processing (QSP). Currently, the primary methods for constructing BEs are the Linear Combination of Unitaries (LCU) and the sparse oracle approach. In this work, we demonstrate that QSP-based techniques, such as Quantum Singular Value Transformation (QSVT) and Quantum Eigenvalue Transformation for Unitary Matrices (QETU), can themselves be efficiently utilized for BE implementation. Specifically, we present several examples of using QSVT and QETU algorithms, along with their combinations, to block encode Hamiltonians for lattice bosons, an essential ingredient in simulations of high-energy physics. We also introduce a straightforward approach to BE based on the exact implementation of Linear Operators Via Exponentiation and LCU (LOVE-LCU). We find that, while using QSVT for BE results in the best asymptotic gate count scaling with the number of qubits per site, LOVE-LCU outperforms all other methods for operators acting on up to $\lesssim11$ qubits, highlighting the importance of concrete circuit constructions over mere comparisons of asymptotic scalings. Using LOVE-LCU to implement the BE, we simulate the time evolution of single-site and two-site systems in the lattice $\varphi^4$ theory using the Generalized QSP algorithm and compare the gate counts to those required for Trotter simulation. |
| format | Article |
| id | doaj-art-4f4166deb4f7414abd65dc08d6ca22d7 |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-4f4166deb4f7414abd65dc08d6ca22d72025-08-20T03:54:01ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-05-019174710.22331/q-2025-05-15-174710.22331/q-2025-05-15-1747Block encoding bosons by signal processingChristopher F. KaneSiddharth HariprakashNeel S. ModiMichael KreshchukChristian W BauerBlock Encoding (BE) is a crucial subroutine in many modern quantum algorithms, including those with near-optimal scaling for simulating quantum many-body systems, which often rely on Quantum Signal Processing (QSP). Currently, the primary methods for constructing BEs are the Linear Combination of Unitaries (LCU) and the sparse oracle approach. In this work, we demonstrate that QSP-based techniques, such as Quantum Singular Value Transformation (QSVT) and Quantum Eigenvalue Transformation for Unitary Matrices (QETU), can themselves be efficiently utilized for BE implementation. Specifically, we present several examples of using QSVT and QETU algorithms, along with their combinations, to block encode Hamiltonians for lattice bosons, an essential ingredient in simulations of high-energy physics. We also introduce a straightforward approach to BE based on the exact implementation of Linear Operators Via Exponentiation and LCU (LOVE-LCU). We find that, while using QSVT for BE results in the best asymptotic gate count scaling with the number of qubits per site, LOVE-LCU outperforms all other methods for operators acting on up to $\lesssim11$ qubits, highlighting the importance of concrete circuit constructions over mere comparisons of asymptotic scalings. Using LOVE-LCU to implement the BE, we simulate the time evolution of single-site and two-site systems in the lattice $\varphi^4$ theory using the Generalized QSP algorithm and compare the gate counts to those required for Trotter simulation.https://quantum-journal.org/papers/q-2025-05-15-1747/pdf/ |
| spellingShingle | Christopher F. Kane Siddharth Hariprakash Neel S. Modi Michael Kreshchuk Christian W Bauer Block encoding bosons by signal processing Quantum |
| title | Block encoding bosons by signal processing |
| title_full | Block encoding bosons by signal processing |
| title_fullStr | Block encoding bosons by signal processing |
| title_full_unstemmed | Block encoding bosons by signal processing |
| title_short | Block encoding bosons by signal processing |
| title_sort | block encoding bosons by signal processing |
| url | https://quantum-journal.org/papers/q-2025-05-15-1747/pdf/ |
| work_keys_str_mv | AT christopherfkane blockencodingbosonsbysignalprocessing AT siddharthhariprakash blockencodingbosonsbysignalprocessing AT neelsmodi blockencodingbosonsbysignalprocessing AT michaelkreshchuk blockencodingbosonsbysignalprocessing AT christianwbauer blockencodingbosonsbysignalprocessing |